Main menu

Tag Archives: pi

Today is Pi Day (3.14.15). Pi is not a person. But it is very interesting.

The people who initiated the hunt for pi were the Babylonians and Egyptians, nearly 4000 years ago. They found that pi was slightly greater than 3, and came up with the value 3 1/8 or 3.125. At around 1650 BC, a scribe named Ahmes implied in the Rhind Papyrus that pi = 4(8/9)2 = 3.16049, which is also fairly accurate. The next approximation of pi is found in the Old Testament. 1 Kings 7:23, says: “Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.” This implies that pi = 3.

The first man to really make an impact in the calculation of pi was the Greek, Archimedes of Syracuse. Archimedes fapproximated the circle’s circumference instead of the area. He started with an inscribed and a circumscribed hexagon, then doubled the sides four times to finish with two 96-sided polygons. The earliest value of pi used in China was 3. In 263 AD, Liu Hui arrived at the value pi = 3.14159, which are the correct first five digits. Near the end of the 5th century, Tsu Ch’ung-chih and his son Tsu Keng-chih calculated 3.1415926 < pi < 3.1415927. Soon after, the Hindu mathematician Aryabhata gave the ‘accurate’ value 62,832/20,000 = 3.141. Another Indian mathematician, Brahmagupta, calculated pi would approach the square root of 10 [=3.162…].

In 1593, Adrianus Romanus used a circumscribed polygon with 230 sides to compute pi to 17 digits after the decimal, of which 15 were correct. Just three years later, Ludolph Van Ceulen presented 20 digits, and by the time he died in 1610, he had accurately found 35 digits. These digits were cut into his tombstone in St. Peter’s Churchyard in Leyden. In 1873, an Englishman named William Shanks used the formula to calculate 707 places of pi, but only the first 527 digits were correct. Johann Heinrich Lambert proved the irrationality of pi first in 1761 and then in more detail in 1767. In 1882, Ferdinand von Lindemann proved the transcendence of pi. Since this means that pi is not a solution of any algebraic equation, it lay to rest the uncertainty about squaring the circle.

In the twentieth century, computers allowed mathematicians to get to previously incomprehensible results. In 1947, D. F. presented 808 digits of pi. One and a half years later, Levi Smith and John Wrench hit the 1000-digit-mark . Finally, in 1949, the ENIAC (Electronic Numerical Integrator and Computer) was finally functional, the gigantic machine calculated 2037 digits in just seventy hours. John Wrench and Daniel Shanks found 100,000 digits in 1961, and the one-million-mark was surpassed in 1973.

Just thirty-nine decimal places would be enough to compute the circumference of a circle surrounding the known universe to within the radius of a hydrogen atom. At the present time, the only tangible application for all those digits is to test computers and computer chips for bugs.

March 14th has long been considered to be “pi” day, celebrated by eating pies (and maybe doing some Math. There are some wild and hardcore partiers out there). This is my favorite recipe, by Rose Levy Beranbaum, from her book The Baking Bible. Her other book, The Bread Bible, is my favorite cookbook of all time. We’re talking serious breads, scones, cakes. But here is the- dare I say- perfect pie recipe: